A consonant class scale is a scale with a consonant interval class, that is, a number n such that all n-step intervals of the scale are "consonances" (of a certain odd limit).

The models for such scales are meantone[5] (in which the 2-step intervals are 5/4 and 4/3), and even better known, meantone[7] (in which the 2-step intervals are 6/5 and 5/4). Harmonizing a diatonic melody by parallel thirds is a commonly used formula that reliably produces beautiful harmony. Consonant class scales are an attempt to generalize this property of the diatonic scale.

Rank-2 consonant class scales

3-limit

{4/3, 3/2}

Augmented[6] (3-step intervals consist of 3 4/3's and 3 3/2's)

5-limit

{6/5, 5/4}

Meantone[7] (2-step intervals consist of 4 6/5's and 3 5/4's)
Porcupine[7] (2-step intervals consist of 5 6/5's and 2 5/4's)
Mavila[7] (2-step intervals consist of 3 6/5's and 4 5/4's)
Srutal[10] (3-step intervals consist of 4 6/5's and 6 5/4's)
Negri[10] (3-step intervals consist of 3 6/5's and 7 5/4's)
Blackwood[10] (3-step intervals consist of 5 6/5's and 5 5/4's)
Sensi[11] (3-step intervals consist of 9 6/5's and 2 5/4's)
Orson[13] (4-step intervals consist of 3 6/5's and 10 5/4's)
Godzilla[14] (4-step intervals consist of 8 6/5's and 6 5/4's)
Helmholtz[17] (5-step intervals consist of 8 6/5's and 9 5/4's)
Superpyth[17] (5-step intervals consist of 9 6/5's and 8 5/4's)

{6/5, 4/3}

Mavila[5] (2-step intervals consist of 1 6/5 and 4 4/3's)
Hanson[7] (2-step intervals consist of 6 6/5's and 1 4/3)
Srutal[8] (3-step intervals consist of 2 6/5's and 6 4/3's)
Doublewide[10] (3-step intervals consist of 8 6/5's and 2 4/3's)

{5/4, 4/3}

Meantone[5] (2-step intervals consist of 1 5/4 and 4 4/3's)
Porcupine[8] (3-step intervals consist of 3 5/4's and 5 4/3's)
Diminished[8] (3-step intervals consist of 4 5/4's and 4 4/3's)
Mohajira/Maqamic[10] (4-step intervals consist of 2 5/4's and 8 4/3's)
Hanson[11] (4-step intervals consist of 6 5/4's and 5 4/3's)
Tetracot[13] (5-step intervals consist of 4 5/4's and 9 4/3's)

7-limit

{8/7, 7/6}

Slendric[5] (1-step intervals consist of 4 8/7's and 1 7/6)
Superpyth[5] (1-step intervals consist of 3 8/7's and 2 7/6's)
Orwell[9] (2-step intervals consist of 1 8/7 and 8 7/6's)
Miracle[10] (2-step intervals consist of 8 8/7's and 2 7/6's)
Pajara[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
Beatles/Maqamic/Hemif[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
Hedgehog[14] (3-step intervals consist of 4 8/7's and 10 7/6's)
Porcupine[15] (3-step intervals consist of 9 8/7's and 6 7/6's)
Augene[15] (3-step intervals consist of 6 8/7's and 9 7/6's)
Meantone[19] (4-step intervals consist of 9 8/7's and 10 7/6's)
Sensi[19] (4-step intervals consist of 6 8/7's and 13 7/6's)

{8/7, 6/5}

Keemun[4] (aka magical seventh chord)
Gorgo[5] (1-step intervals consist of 4 8/7's and 1 6/5)
Porcupine[8] (2-step intervals consist of 2 8/7's and 6 6/5's)
Armodue[9] (2-step intervals consist of 4 8/7's and 5 6/5's)
Negri[9] (2 step intervals consist of 7 8/7's and 2 6/5's)
Astrology[10] (2-step intervals consist of 8 8/7's and 2 6/5's)
Maqamic[10] (2-step intervals consist of 6 8/7's and 4 7/6's)
Flattone[12] (3-step intervals consist of 3 8/7's and 9 6/5's)
Magic[16] (4-step intervals consist of 4 8/7's and 12 6/5's)
Mohajira[17] (4-step intervals consist of 6 8/7's and 11 6/5's)

{8/7, 5/4}

Hemithirds[7] (2-step intervals consist of 5 5/4's and 2 8/7's)
Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
Magic[13] (4-step intervals consist of 1 8/7 and 12 5/4's)

{7/6, 6/5}

Myna[4] (aka starling tetrad)
Sensi[8] (2-step intervals consist of 2 7/6's and 6 6/5's)
Hedgehog[8] (2-step intervals consist of 4 7/6's and 4 6/5's)
Superpelog[9] (2-step intervals consist of 8 7/6's and 1 6/5)
Negri[9] (2 step intervals consist of 7 7/6's and 2 6/5's)
Meantone[12] (3-step intervals consist of 3 7/6's and 9 6/5's)
Augene[12] (3-step intervals consist of 3 7/6's and 9 6/5's)
Pajara[12] (3-step intervals consist of 6 7/6's and 6 6/5's)
Valentine[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
Muggles[16] (4-step intervals consist of 4 7/6's and 12 6/5's)
Miracle[21] (5-step intervals consist of 13 7/6's and 8 6/5's)

{7/6, 5/4}

Deutone[7] (2-step intervals consist of 2 7/6's and 5 5/4's)
Godzilla[9] (2-step intervals consist of 8 7/6's and 1 5/4)
Superpyth[12] (3-step intervals consist of 9 7/6's and 3 5/4's)

{6/5, 9/7}

Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
Superpyth[12] (4-step intervals consist of 4 6/5's and 8 9/7's)

{5/4, 7/5}

Keemun[7] (3-step intervals consist of 2 5/4's and 5 7/5's)

{4/3, 7/5}

Meantone[7] (3-step intervals consist of 6 4/3's and 1 7/5; both 2-step intervals are also consonant)
Beatles[7] (3-step intervals consist of 5 4/3's and 2 7/5')
Negri[9] (4-step intervals consist of 5 4/3's and 4 7/5's)
Sensi[11] (5-step intervals consist of 4 4/3's and 7 7/5's)
Miracle[11] (5-step intervals consist of 5 4/3's and 6 7/5's)
Magic[16] (7-step intervals consist of 11 4/3's and 5 7/5's)

{4/3, 10/7}

Garibaldi[7] (3-step intervals consist of 6 4/3's and 1 10/7)
Dominant[7] (3-step intervals consist of 6 4/3's and 1 10/7)
Augene[9] (4-step intervals consist of 6 4/3's and 3 10/7's)
Godzilla[9] (4-step intervals consist of 7 4/3's and 2 10/7's)
Superpyth[12] (5-step intervals consist of 11 4/3's and 1 10/7)
Muggles[13] (6-step intervals consist of 8 4/3's and 5 10/7's)
Rodan[21] (9-step intervals consist of 18 4/3's and 3 10/7's)

{7/5, 10/7}

Hemithirds[6] (3-step intervals consist of 3 7/5's and 3 10/7's)
Miracle[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
Beatles[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
Negri[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
Blacksmith[10] (5-step intervals consist of 5 7/5's and 5 10/7's)
Meantone[12] (6-step intervals consist of 6 7/5's and 6 10/7's)
Augene[12] (6-step intervals consist of 6 7/5's and 6 10/7's)
Muggles[16] (8-step intervals consist of 8 7/5's and 8 10/7's)
Superpyth[22] (11-step intervals consist of 11 7/5's and 11 10/7's)

9-limit

{7/6, 9/7}

Superpyth[7] (2-step intervals consist of 3 9/7's and 4 7/6's)

{6/5, 9/7}

Sensamagic, Godzilla[9] (3-step intervals consist of 3 6/5's and 6 9/7's)
Hedgehog[6] (2-step intervals consist of 2 6/5's and 4 9/7's)

{5/4, 9/7}

Orwell[9] (3-step intervals consist of 6 5/4's and 3 9/7's)
Negri[9] (3-step intervals consist of 6 5/4's and 3 9/7's)
Meantone[12] (4-step intervals consist of 8 5/4's and 4 9/7's)
Pajara[12] (4-step intervals consist of 8 5/4's and 4 9/7's)
Miracle[21] (7-step interval consists of 14 5/4's and 7 9/7's)

{9/7, 4/3}

Semaphore[5] (2-step intervals consist of 2 9/7's and 3 4/3's)
Superpyth[5] (2-step intervals consist of 1 9/7 and 4 4/3's)
Diminished[8] (3-step intervals consist of 4 9/7's and 4 4/3's)
Sensi[8] (3-step intervals consist of 7 9/7's and 1 4/3)
Hedgehog[8] (3-step intervals consist of 6 9/7's and 2 4/3's)
Beatles/Hemif/Maqamic[10] (4-step intervals consist of 2 9/7's and 8 4/3's)
Pajara[10] (4-step intervals consist of 2 9/7's and 8 4/3's)
Negri[10] (4-step intervals consist of 4 9/7's and 6 4/3's)
Orwell[13] (5-step intervals consist of 7 9/7's and 6 4/3's)
Keemun[15] (6-step intervals consist of 6 9/7's and 9 4/3's)
Augene[15] (6-step intervals consist of 3 9/7's and 12 4/3's)
Mohajira[17] (7-step intervals consist of 2 9/7's and 17 4/3's)

{9/7, 7/5}

Deutone[7] (3-step intervals consist of 4 7/5's and 3 9/7's)
Magic[13] (5-step intervals consist of 11 9/7's and 2 7/5's)

{9/7,10/7}

Muggles[10] (5-step intervals consist of 8 9/7's and 2 10/7's)

{9/7, 3/2}

Magic[7] (3-step intervals consist of 5 9/7's and 2 3/2's)

3.5.7-subgroup

{9/7, 7/5}

Sirius[7] (2-step intervals consist of 2 9/7's and 5 7/5's)

{7/5, 5/3}

Rank-2 Bohlen-Pierce[5] (2-step intervals consist of 2 7/5's and 3 5/3's)

{5/3, 9/5}

Sirius[6] (3-step intervals consist of 3 5/3's and 3 9/5's)

Rank-3 consonant class scales

7-limit

{8/7, 6/5, 5/4}

Marvel, marvel11max7a and marvel11max7b, 7 notes (2-step intervals consist of 1 8/7, 2 6/5's, and 4 5/4's)

{7/6, 6/5, 5/4}

Hewuermity or Zeus, zeus7tri, 7 notes (2-step intervals consist of 2 7/6's, 1 6/5, and 4 5/4's)

{5/4, 4/3, 7/5}

Breed or Jove, 7 notes (3-step intervals consist of 2 5/4's, 1 4/3, and 4 7/5's)

{7/6, 6/5, 5/4}

Portent; 4 5/4's 4 6/5's and 3 7/6's in the third class

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Theory

Consonant class scale

Rank-2 consonant class scales

3-limit

{4/3, 3/2}

5-limit

{6/5, 5/4}

{6/5, 4/3}

{5/4, 4/3}

7-limit

{8/7, 7/6}

{8/7, 6/5}

{8/7, 5/4}

{7/6, 6/5}

{4/3, 7/5}

{4/3, 10/7}

{7/5, 10/7}

9-limit

{7/6, 9/7}

{6/5, 9/7}

{5/4, 9/7}

{9/7, 4/3}

{9/7, 7/5}

{9/7,10/7}

{9/7, 3/2}

3.5.7-subgroup

{9/7, 7/5}

{7/5, 5/3}

{5/3, 9/5}

Rank-3 consonant class scales

7-limit

{8/7, 6/5, 5/4}

{7/6, 6/5, 5/4}

{5/4, 4/3, 7/5}

{7/6, 6/5, 5/4}

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